Problem - Approx. two weeks ago, we began to experience a decrease in Hot water pressure. Pressure is okay for about 10-15 secs and then we experience a steady decrease in pressure on any and all faucets. Cold water is okay.

House in on crawl space.

Question - Is it possible that this problem could be caused by a leak on the common output side of the Hot Water Heater? Is it also possible that there is a leak on the common Cold Water input side of the water heater .

A galvaized nipple on the outlet of the WH which has corroded internally could cause exactly this. With no flow, you have full pressure throughout the piping. But as you try to draw hot water, the pressure drops down because of the restriction.

I once had a problem where the screw that attached the washer to a globe valve corroded off and left the washer loose. The washer would let a little water pass until the flow got it into a position in the valve that restricted flow.

Any kind of loose material too large to pass but large enough to restrict flow could cause that. One suspect would be the tempering valve which has some pretty small passages.